Occupancy Models - Introduction to Ecological Sampling - page 127

for the status of the species across different points of the landscape are insuf-
ficient. Royle and Link (2005) considered a situation for which four categories
of relative abundance were of interest based on call-index data for breeding
amphibians. Nichols et al . (2007) considered a situation for which three cat-
egories were of interest for assessing the amount of successful reproduction
of California spotted owls ( Stryx occidentalis occidentalis ) at a study site in the
U.S. Sierra Nevada mountains, where the categories of interest were absent,
present without successful reproduction, and present with successful repro-
duction. In each case, there was potential for one-way misclassification. For
example, registering calls from a few individuals precludes the possibility of
the species being absent, but a greater number of individuals may have been
present at the sample unit with some going undetected. Although Royle and
Link (2005) and Nichols et al. (2007) used different parameterizations, the
underlying modeling framework was the same, as noted by MacKenzie et
al. (2009). Details of the different parameterizations are not given here, and
readers are directed to the articles cited. A rather general parameterization
is used in the following material, but it is noted that other parameterizations
can be used and are likely to be more reasonable for specific applications.
In the multiple-category situation, the outcome of each survey can be
recorded as a 0, 1, 2, and so on, rather than just a 0 or 1 as for the two-cat-
egory situation. A similar approach to the two-category model is used by
which any ambiguity in the detection history is resolved by adding together
the probabilities to the individual outcomes. Technically, this procedure is
known as integrating across the possible occupancy states. For example, if
the parameters were defined as

φ [] is the probability of a unit being of category m , and
p j lm

[, ]

is the probability of observing evidence of category l in the j th
survey, given the unit is truly of category m ,

the probability statement for the detection history 021 would be

( )

[2] [0,2] [2,2] [1,2]

Pr h = 021 = φ p pp .

i 1 2 3

For example, in the context of the three categories being the presence of the
species with and without breeding, the verbal description of this detection
history is the following: “The species is present at the unit and breeding is
occurring there; the species was not detected at all in the first survey; it was
detected in the second survey, and the evidence of reproduction was also
observed; then in the third survey the species was detected but there was
no evidence of reproduction.” In this case, there is no ambiguity associated
with the detection history as the evidence of breeding (i.e., a 2) was observed
at least once during the surveys, confirming that breeding was occurring.